Working in the context of symmetric spectra, we consider any higher algebraic structures that can be described as algebras over an operad O. We prove that the fundamental adjunction comparing O-algebra spectra with coalgebra spectra over the associated comonad K, via topological Quillen homology (or TQ-homology), can be turned into an equivalence of homotopy theories by replacing O-algebras wit...

In this paper, we give three functors $mathfrak{P}$, $[cdot]_K$ and $mathfrak{F}$ on the category of C$^ast$-algebras. The functor $mathfrak{P}$ assigns to each C$^ast$-algebra $mathcal{A}$ a pre-C$^ast$-algebra $mathfrak{P}(mathcal{A})$ with completion $[mathcal{A}]_K$. The functor $[cdot]_K$ assigns to each C$^ast$-algebra $mathcal{A}$ the Cauchy extension $[mathcal{A}]_K$ of $mathcal{A}$ by ...

Let $A$ be a Banach algebra and $E$ be a Banach $A$-bimodule then $S = A oplus E$, the $l^1$-direct sum of $A$ and $E$ becomes a module extension Banach algebra when equipped with the algebras product $(a,x).(a^prime,x^prime)= (aa^prime, a.x^prime+ x.a^prime)$. In this paper, we investigate $triangle$-amenability for these Banach algebras and we show that for discrete inverse semigroup $S$ with...

in this paper, the main results are:a study of the finitely generated mv-algebras of continuous functions from the n-th power of the unit real interval i to i;a study of hopfian mv-algebras; anda category-theoretic study of the map sending an mv-algebra as above to the range of its generators (up to a suitable form of homeomorphism).

We show that, if A is a finite-dimensional *-simple associative algebra with involution (over the field K of real or complex numbers) whose hermitian part H( A, * > is of degree > 3 over its center, if B is a unital algebra with involution over 06, and if (I.11 is an algebra norm on H( A @ B, * 1, then there exists an algebra norm on A @ B whose restriction to H(A @ B, *> is equivalent to 11 . ...

The R12 h matrices of the Jordanian Uh(sl(2)) algebra at arbitrary dimensions may be obtained from the corresponding Rj1;j2 q matrices of the standard q-deformed Uq(sl(2)) algebra through a contraction technique. By extending this method, the coloured two-parametric (h, α) Jordanian R1122 h,α matrices of the Uh,α(gl(2)) algebra may be derived from the corresponding coloured R j1,z1;j2,z2 q,λ ma...

In this paper, we study how two important ideals of a given Lie algebra g (namely, the center Z(g) and the derived Lie algebra D(g)) can be translated into the language of Graph Theory. In this way, we obtain some criteria and characterizations of these ideals using Graph Theory.

A classical Lagrangian formalism has recently been given ~1 from which both the symmetrized set of Maxwell’s equations and the equations of motion for both electrically and magnetically charged particles can be derived. This analysis uses two potentials, following Cabibbo and Ferrari, [‘I and employs space-time algebra,#’ the Clifford algebra appropriate to four-dimensional Minkowski space-time...

After reviewing the recent results on the Drinfeld realization of the face type elliptic quantum group Bq,λ(ŝlN ) by the elliptic algebra Uq,p(ŝlN ), we investigate a fusion of the vertex operators of Uq,p(ŝlN ). The basic generating functions Λj(z) (1 ≤ j ≤ N − 1) of the deformed WN algebra are derived explicitly.

For a finite quiver without sources or sinks, we prove that the homotopy category of acyclic complexes of injective modules over the corresponding finite-dimensional algebra with radical square zero is triangle equivalent to the derived category of the Leavitt path algebra viewed as a differential graded algebra with trivial differential, which is further triangle equivalent to the stable categ...